{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib.pylab import plt\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import statsmodels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's start with some informal exploration"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "air_passengers = pd.read_csv(\"./data/AirPassengers.csv\", header = 0, parse_dates = [0], names = ['Month', 'Passengers'], index_col = 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Passengers</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-01-01</th>\n",
       "      <td>112</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-03-01</th>\n",
       "      <td>132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-04-01</th>\n",
       "      <td>129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1949-05-01</th>\n",
       "      <td>121</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Passengers\n",
       "Month                 \n",
       "1949-01-01         112\n",
       "1949-02-01         118\n",
       "1949-03-01         132\n",
       "1949-04-01         129\n",
       "1949-05-01         121"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "air_passengers.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Is this the behavior I want?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Passengers</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Passengers\n",
       "Month                 \n",
       "1949-02-01         118"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "air_passengers['1949-01-05':'1949-02-17']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# How do we get the desired behavior?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Passengers</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1949-02-01</th>\n",
       "      <td>118</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            Passengers\n",
       "Month                 \n",
       "1949-02-01         118"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "air_passengers['1949-01-05':'1949-02-17']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Think about what your data means. Pandas can't do the thinking for you"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d3d2a72160>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IiJRQoaGISArl5+dn+hSkikvmvzEFBSIiKdC8eXPq16/P1VdfnelTkWqgfv36NG/ePOHP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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d3d2a6bef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "air_passengers.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d3d2b37a20>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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dgMeASyJivVb3SJKkoVl3BO7z48CCzHxPr2V39dvmGGB2Zv4YICIOBRYCBwLf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\nW6ld1WPbNkR1P9DwfmC3Qdb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sjXM/bwc+a5dtdW0rtcu2+rWV2mXbMHs68SS08cle0evJ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\nkiTAUCBJkipDgSRJAgwFkiSp+gR53jsYac3ZTAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d3d2b40908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "air_passengers['1950'].plot(kind = 'bar')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d3d2ba3e80>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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BJEnN0bQtBZIkKS++94EkSQIcCiRJUuGNcp6CNRIRe1A7U2LriZGeAm5LKd3R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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d3d3bbc6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "air_passengers['1951'].plot(kind = 'bar')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Getting a little more formal\n",
    "### first thing we look at for a time series when we want to use common analysis techniques:\n",
    "### is it stationary: mean, variance, autocovariance do not depend on time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d3d2a1e048>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jpEBERAA/ZuDii+Gkk2DhQjj++KAjktKmpEBERHj1VejUCVq3hg8+8CsVSvxR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\nAhEREQGUFIiIiEjI/wPeDEcN1r3K1wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1d3d3d9db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# first test, informally, plot the moving average\n",
    "# note the ROLLING function\n",
    "air_passengers.rolling(window = 60).mean().plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# How can we see whether the variance changes over time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Can you plot the autocorrelation?\n",
    "from statsmodels.tsa.stattools import acf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# What is the autocorrelation and how can we visualize it? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How can I see whether the autocorrelation is changing over time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# What would we do differently from above?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Always have to make judgment calls"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# How should you size your window?\n",
    "air_passengers.rolling(window = 120).var().plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# And now let's make it formal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# next more formally apply the Augmented Dickey-Fuller test\n",
    "from statsmodels.tsa.stattools import adfuller\n",
    "adfuller(air_passengers.Passengers, autolag = 'AIC', regression = 'ct')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### What do these numbers mean? Let's take a look at statsmodels documentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Can we write a function to output these #s sensibly?\n",
    "# Check out statsmodels.sourceforge.net/devel/generated/statsmodels.tsa.stattools.adfuller.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Where do we go from here?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Are we stuck not doing any analysis now that our time series is not stationary? Hint: no.\n",
    "# How can we make it stationary?\n",
    "# Why is it non-stationary (2 reasons)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# One method to get rid of time varying variance is to do a power or log transformation that punishes larger values\n",
    "# more than smaller values\n",
    "log_passengers = air_passengers.Passengers.apply(lambda x: np.log(x))\n",
    "log_passengers.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Let's see what that looks like as a power transformation\n",
    "rt_passengers = air_passengers.Passengers.apply(lambda x: x**.5)\n",
    "rt_passengers.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# This reduces the variance in variance as opposed to the original trend\n",
    "air_passengers.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# However there is still a trend we need to remove\n",
    "# Let's calculate a rolling mean\n",
    "# Experiment with window size\n",
    "air_passengers.rolling(window = 12).mean().plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# What if we subtract this rolling mean from the original series?\n",
    "rolling_mean = air_passengers.rolling(window = 12).mean()\n",
    "passengers_detrended = air_passengers - rolling_mean\n",
    "passengers_detrended.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Exercise: try detrending after taking the log. How does that look?\n",
    "log_rolling_mean = log_passengers.rolling(window = 12).mean()\n",
    "log_detrended = log_passengers - log_rolling_mean\n",
    "log_detrended.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "log_detrended.rolling(20).median().plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Exercise: try detrending before taking the log. How does that look?\n",
    "rolling_mean = air_passengers.rolling(window = 12).mean()\n",
    "passengers_detrended = air_passengers - rolling_mean\n",
    "log_detrended2 = passengers_detrended.Passengers.apply(lambda x: np.log(x))\n",
    "log_detrended2.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why didn't that work?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Now let's use a regression rather than a rolling mean to detrend\n",
    "from statsmodels.regression.linear_model import OLS\n",
    "model = OLS(air_passengers.Passengers.values, list(range(len(air_passengers.values))))\n",
    "result = model.fit()\n",
    "result.params\n",
    "fit = pd.Series(result.predict(list(range(len(air_passengers.values)))), index = air_passengers.index)\n",
    "\n",
    "passengers_detrended = air_passengers.Passengers - fit\n",
    "passengers_detrended.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "passengers_detrended.rolling(20).median().plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What worked better, the rolling average or the regression? Why?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "# Seasonality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Differencing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "(air_passengers.Passengers - air_passengers.Passengers.shift()).plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# One common technique is differencing, let's start with log_passengers\n",
    "log_passengers_diff = log_passengers - log_passengers.shift()\n",
    "log_passengers_diff.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Let's again test for stationarity with a gut level check.\n",
    "# And let's write a function to do it since this seems like something we'll have to do a lot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "log_passengers = log_passengers.to_timestamp()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from statsmodels.tsa.seasonal import seasonal_decompose\n",
    "\n",
    "log_passengers.interpolate(inplace = True)\n",
    "decomposition = seasonal_decompose(log_passengers, model = 'multiplicative')\n",
    "decomposition.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Seasonal or multiplicative time series?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# When to use which?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "decomposition = seasonal_decompose(log_passengers, model = 'multiplicative')\n",
    "trend = decomposition.trend\n",
    "seasonal = decomposition.seasonal\n",
    "residual = decomposition.resid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(log_passengers, label='Original')\n",
    "plt.plot(trend, label='Trend')\n",
    "plt.plot(seasonal,label='Seasonality')\n",
    "plt.plot(residual, label='Residuals')\n",
    "plt.legend(loc = 'best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Let's walk through seasonal_decompose"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "from statsmodels.compat.python import lmap, range, iteritems\n",
    "import numpy as np\n",
    "from pandas.core.nanops import nanmean as pd_nanmean\n",
    "from statsmodels.tsa.filters._utils import _maybe_get_pandas_wrapper_freq\n",
    "from statsmodels.tsa.filters.filtertools import convolution_filter\n",
    "from statsmodels.tsa.tsatools import freq_to_period\n",
    "\n",
    "def seasonal_decompose(x, model=\"additive\", filt=None, freq=None, two_sided=True):\n",
    "    \"\"\"\n",
    "    Seasonal decomposition using moving averages\n",
    "    Parameters\n",
    "    ----------\n",
    "    x : array-like\n",
    "        Time series\n",
    "    model : str {\"additive\", \"multiplicative\"}\n",
    "        Type of seasonal component. Abbreviations are accepted.\n",
    "    filt : array-like\n",
    "        The filter coefficients for filtering out the seasonal component.\n",
    "        The concrete moving average method used in filtering is determined by two_sided.\n",
    "    freq : int, optional\n",
    "        Frequency of the series. Must be used if x is not  a pandas object.\n",
    "        Overrides default periodicity of x if x is a pandas\n",
    "        object with a timeseries index.\n",
    "    two_sided : bool\n",
    "        The moving average method used in filtering.\n",
    "        If True (default), a centered moving average is computed using the filt.\n",
    "        If False, the filter coefficients are for past values only.\n",
    "    Returns\n",
    "    -------\n",
    "    results : obj\n",
    "        A object with seasonal, trend, and resid attributes.\n",
    "    Notes\n",
    "    -----\n",
    "    This is a naive decomposition. More sophisticated methods should\n",
    "    be preferred.\n",
    "    The additive model is Y[t] = T[t] + S[t] + e[t]\n",
    "    The multiplicative model is Y[t] = T[t] * S[t] * e[t]\n",
    "    The seasonal component is first removed by applying a convolution\n",
    "    filter to the data. The average of this smoothed series for each\n",
    "    period is the returned seasonal component.\n",
    "    See Also\n",
    "    --------\n",
    "    statsmodels.tsa.filters.bk_filter.bkfilter\n",
    "    statsmodels.tsa.filters.cf_filter.xffilter\n",
    "    statsmodels.tsa.filters.hp_filter.hpfilter\n",
    "    statsmodels.tsa.filters.convolution_filter\n",
    "    \"\"\"\n",
    "    _pandas_wrapper, pfreq = _maybe_get_pandas_wrapper_freq(x)\n",
    "    x = np.asanyarray(x).squeeze()\n",
    "    nobs = len(x)\n",
    "\n",
    "    if not np.all(np.isfinite(x)):\n",
    "        raise ValueError(\"This function does not handle missing values\")\n",
    "    if model.startswith('m'):\n",
    "        if np.any(x <= 0):\n",
    "            raise ValueError(\"Multiplicative seasonality is not appropriate \"\n",
    "                             \"for zero and negative values\")\n",
    "\n",
    "    if freq is None:\n",
    "        if pfreq is not None:\n",
    "            pfreq = freq_to_period(pfreq)\n",
    "            freq = pfreq\n",
    "        else:\n",
    "            raise ValueError(\"You must specify a freq or x must be a \"\n",
    "                             \"pandas object with a timeseries index with\"\n",
    "                             \"a freq not set to None\")\n",
    "\n",
    "    if filt is None:\n",
    "        if freq % 2 == 0:  # split weights at ends\n",
    "            filt = np.array([.5] + [1] * (freq - 1) + [.5]) / freq\n",
    "        else:\n",
    "            filt = np.repeat(1./freq, freq)\n",
    "\n",
    "    nsides = int(two_sided) + 1\n",
    "    trend = convolution_filter(x, filt, nsides)\n",
    "\n",
    "    # nan pad for conformability - convolve doesn't do it\n",
    "    if model.startswith('m'):\n",
    "        detrended = x / trend\n",
    "    else:\n",
    "        detrended = x - trend\n",
    "\n",
    "    period_averages = seasonal_mean(detrended, freq)\n",
    "\n",
    "    if model.startswith('m'):\n",
    "        period_averages /= np.mean(period_averages)\n",
    "    else:\n",
    "        period_averages -= np.mean(period_averages)\n",
    "\n",
    "    seasonal = np.tile(period_averages, nobs // freq + 1)[:nobs]\n",
    "\n",
    "    if model.startswith('m'):\n",
    "        resid = x / seasonal / trend\n",
    "    else:\n",
    "        resid = detrended - seasonal\n",
    "\n",
    "    results = lmap(_pandas_wrapper, [seasonal, trend, resid, x])\n",
    "    return DecomposeResult(seasonal=results[0], trend=results[1],\n",
    "                           resid=results[2], observed=results[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = log_passengers\n",
    "_pandas_wrapper, pfreq = _maybe_get_pandas_wrapper_freq(x)\n",
    "model = \"multiplicative\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.asanyarray(x).squeeze()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "nobs = len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "nobs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "if not np.all(np.isfinite(x)):\n",
    "    raise ValueError(\"This function does not handle missing values\")\n",
    "if model.startswith('m'):\n",
    "    if np.any(x <= 0):\n",
    "        raise ValueError(\"Multiplicative seasonality is not appropriate \"\n",
    "                             \"for zero and negative values\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "freq = None\n",
    "if freq is None:\n",
    "    if pfreq is not None:\n",
    "        pfreq = freq_to_period(pfreq)\n",
    "        freq = pfreq\n",
    "    else:\n",
    "        raise ValueError(\"You must specify a freq or x must be a \"\n",
    "                         \"pandas object with a timeseries index with\"\n",
    "                         \"a freq not set to None\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pfreq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "freq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "filt = None\n",
    "two_sided = True\n",
    "if filt is None:\n",
    "    if freq % 2 == 0:  # split weights at ends\n",
    "        filt = np.array([.5] + [1] * (freq - 1) + [.5]) / freq\n",
    "    else:\n",
    "        filt = np.repeat(1./freq, freq)\n",
    "\n",
    "nsides = int(two_sided) + 1\n",
    "trend = convolution_filter(x, filt, nsides)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(trend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(filt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "if model.startswith('m'):\n",
    "    detrended = x / trend\n",
    "else:\n",
    "    detrended = x - trend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(detrended)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def seasonal_mean(x, freq):\n",
    "    \"\"\"\n",
    "    Return means for each period in x. freq is an int that gives the\n",
    "    number of periods per cycle. E.g., 12 for monthly. NaNs are ignored\n",
    "    in the mean.\n",
    "    \"\"\"\n",
    "    return np.array([pd_nanmean(x[i::freq]) for i in range(freq)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "period_averages = seasonal_mean(detrended, freq)\n",
    "\n",
    "if model.startswith('m'):\n",
    "    period_averages /= np.mean(period_averages)\n",
    "else:\n",
    "    period_averages -= np.mean(period_averages)\n",
    "\n",
    "seasonal = np.tile(period_averages, nobs // freq + 1)[:nobs]\n",
    "\n",
    "if model.startswith('m'):\n",
    "    resid = x / seasonal / trend\n",
    "else:\n",
    "    resid = detrended - seasonal\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "plt.plot(trend)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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